Question: As a trainer for the Canadian Paralympic biathlon team, you are trying to help predict how well an athlete will shoot as a function of how fast that athlete's heart is beating as he or she enters the shooting area. Using sophisticated electronic equipment, you measure the heart rate of all the Paralympic biathletes each time they enter the shooting area in a race and correlate it with how well they shoot. You find a correlation of -0.5. You also find that the mean heart rate is 160 bpm (beats per minute) with a standard deviation of 10 bpm and the mean number of targets hit is 4.2 with a standard deviation of 0.2.

(a) Calculate the regression equation for predicting number of targets hit from heart rate.

(b) Now calculate the predicted number of targets hit for biathletes with a heart rate of \(175\).